One stellar mass is defined as the mass of our sun (1Ms = 1.99 x 1030 kg). ONe astronomical unit is defined as the length of Earth's semi-major axis (1AU = 1.49 x 1011 m). The star Epsilon Eridani in the constellation Eridanus has a planet (discovered in 2000) orbiting it that has a semi-major axis of 3.39 AU. The orbital period of the planet is 6.54 years. Based on this information, determine the mass of Epsilon Eridani in stellar masses (Ms).

BTW, if you want to be precise, you should have used 1 year = 365.242 days, 1 solar mass = 1.98892×1030 kilogram, 1 AU = 1.49598×1011 meters.

However, this will give 0.911 solar masses as the final answer.

If you simply substitute 1.50e11 meters for the length of 1 AU for your value of 1.49e11 meters yields a final answer of 0.919 solar masses. Note well: 1.50e11 meters is a better 3-digit value for the length of 1 AU than is 1.49e11 meters.

So what is going on?

(1) Just because you only know some values to 3 digits does not mean you should truncate everything to 3 digits. It is far better to represent physical constants to their full accuracy and truncate the final result to the expected accuracy (e.g., three digits in this case).

(2) A long sequence of products and ratios involving approximate numbers can (will) reduce the accuracy of your final result.

(3)Raising approximate numbers to powers can (will) reduce the accuracy of your final result.